In the figure, ACCB. D is a point on AB such that CD AB.
Prove that x = y.

The updated positions are (5, -6) + (-2, 10) = (3, 4)

A vector is a mathematical concept that has both magnitude and direction. The vector's size is determined by size. An arrow-depicted line serves as this representation. The vector's magnitude is represented by the line's length, and its direction is shown by the arrow. additionally referred to as geometric, Euclidean, spatial, or just "vectors."

You can add the components of the vector to the corresponding components of the point to translate point (5, -6) based on vector V:(-2,10).

The updated positions are (5, -6) + (-2, 10) = (3, 4)

Thus, the translated message is (3, 4).

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The equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z. The solution has been obtained by using angles and line.

What are angles and line?

Straight lines with little depth or width are present. There are many different types of lines, including perpendicular, intersecting, transversal, etc. A figure called an angle is one in which two rays originate from the same point.

We are given that 2 lines intersect to form 4 angles which are 65°, x°, y°, z°.

1. x° + 65° = 180°

We know that angles on a straight line form a linear pair i.e. their sum is 180°. So, this statement is true.

2. x° = z°

We know that vertically opposite angles are equal. So, x° will be equal to z°. Thus, this statement is true.

3. y° = 65°

We know that vertically opposite angles are equal. So, y will be equal to 65°. Thus, this statement is true.

4. x° = 65°

This statement is false because these are the angles on a straight line which must add up to 180°.

5. x° + y° + z° = 115°

We know that angles in a circle add upto 360°. We know one angle as 65°. So, the remaining angles should add upto 295°. Thus, the statement is false.

Hence, the equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z.

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Question: Which equations are true for the values of x, y, and z? Select three options.

2 lines intersect to form 4 angles as shown in the figure. Clockwise, from top, the angles are: 65 degrees, x, y, z.

x degrees + 65 degrees = 180 degrees

x degrees = z degrees

y degrees = 65 degrees

x degrees = 65 degrees

x degrees + y degrees + z degrees = 115 degrees

Answer:

The solution is 37/30

Step-by-step explanation:

[tex] \sf \frac{2}{15} - ( - \frac{11}{10} ) \\ \\ = \sf \frac{2}{15} + \frac{11}{10} \: \: \: \: \: \: \\ \\ \\ = \sf \frac{2 + 11}{30} \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: = \: \sf \frac{2(2) + 11(3)}{30} \\ \\ = \sf \frac{4 + 33}{30} \: \: \: \: \: \: \: \: \\ \\ = \sf \frac{37}{30} \: or \: 1 \frac{7}{30} \: \: [/tex]

The statement is equivalent to numerical value 81.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is the statement as -

"base 3 and exponent 4"

We can write mathematically as -

{x} = 3⁴

{x} = 3 x 3 x 3 x 3

{x} = 81

Therefore, the statement is equivalent to numerical value 81.

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4A. The number of whole pie shaded are 2

4B . The number of partial pie shaded is 3

4C.  The mixed number formed is 2 3/5

5A. The whole number part which is 2 is the quotient

5B.  The remainder is 3

In mathematics, a fraction is a number that represents a part of a whole. It consists of two parts: a numerator, which is the part of the fraction that represents the number of parts being considered, and a denominator, which is the number that represents the total number of parts in the whole.

A mixed number is a combination of a whole number and a fraction. It represents a quantity that is greater than the fraction but less than the next whole number.

For example, In the division problem, the dividend is 13 and and the divisor is 5. the division results to mixed number of value 2 3/5.

The mixed number 2 3/5 represents a quantity that is equal to

two whole and three fifths.

converting to improper fractions gives 13/5

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Answer: To find the range of the marks obtained, we need to find the difference between the highest and lowest marks:

Range = highest mark - lowest mark

To find the highest and lowest marks, we can simply sort the marks in ascending or descending order:

39, 48, 56, 75, 76, 81, 85, 85, 90, 95

So, the highest mark is 95 and the lowest mark is 39. Then, the range is:

Range = 95 - 39 = 56

To find the mean marks obtained by the group, we need to add up all the marks and divide by the number of marks:

Mean = (85 + 76 + 90 + 85 + 39 + 48 + 56 + 95 + 81 + 75) / 10

   = 745 / 10

   = 74.5

So, the mean marks obtained by the group is 74.5.

Step-by-step explanation:

The proof for the congruence of triangles GHI and GFJ are given below.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

From the figure,

1) Line segment FJ ⊥ line segment FH (given)

2) ∠HGI = ∠FGJ (It is also given)

3) HI = FJ (Given). So HI ≅ FJ

4) HI ⊥ FH (given)

5) Since both the angles F and H are right angles,

∠F ≅ ∠H (since all right angles are congruent)

6) So we get that two angles and a non included side of ΔGHI are equal to the corresponding two angles and a non included side of ΔGFJ.

So by AAS congruence theorem, ΔGHI ≅ ΔGFJ.

Hence the given two triangles are congruent.

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As we can see from graph for given linear inequality -0.25≥-0.5x, the graph will be a number line with a closed circle on 0.5 with an arrow shaded right.

What exactly are linear inequalities?

Inequality is a mathematical statement in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers. The equal sign "=" in the phrase is substituted by any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠). In mathematics, there are three types of inequalities: polynomial inequalities, rational inequalities, and absolute value inequalities.

The symbols "< and '>' represent severe inequalities, whereas  ‘≤’ and ‘≥’  represent slack inequalities. A linear inequality appears to be the same as a linear equation, however there is a difference.

Now,

Given linear inequality is -0.25≥-0.5x

0.25≤0.5x

1/4≤1/2x

x≥1/2

hence,

        graph will be a number line with a closed circle on 0.5 with an arrow shaded right.

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The required value of the x to the nearest tenth is given as x = 8.8. Option C is correct.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal 180°

Here,
Since the question seems to be incomplete, the complete question has been attached at the last of the solution,

Now, A triangle is shown in the image attached,

To evaluate the measure of x, we apply the sine rule,
8.2/(sin(180-126-28)) = x/sin28
8.2/sin26 = x/sin28
x = 8.2sin28/sin26
x = 8.8

Thus, the required value of the x to the nearest tenth is given as x = 8.8. Option C is correct.

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Answer:

x= 39.549°

Step-by-step explanation:

please review answer.

Answer:

Step-by-step explanation:

The formula for the Area of a square is:

A=[tex]s^{2}[/tex] Where s is the length of the side of the square.

Substituting and solving for s gives:

64 units2  = [tex]s^{2}[/tex]

√64 units2 =√s2

8 units =  s

The formula for the perimeter of a square is:

p=4s

Where s is the length of the side of the square.

Answer:

x[tex]\leq[/tex]52

Step-by-step explanation:

x[tex]\leq[/tex]52

The value for  x-5(x - 1)=x- (2x-3) which gives x = 2/3.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

x-5(x - 1)=x- (2x-3)

Now, solving the Equation for x we get

x -5x + 5 = x - 2x + 3

-4x + 5 = -x + 3

-4x + x = 3 -5

-3x = -2

x= 2/3

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Answer: badkid jay

Step-by-step explanation: because he gets him everything he ask for and shows favoritism towards him

Answer:

Step-by-step explanation:

PennyWise

NickleSmart

DimeSharp

QuarterIntelligent

The solution to the equation 6(72(x - 2)) = 4(15 - 3x) is x = 77/37.

Given the equation in the question

6(72(x - 2)) = 4(15 - 3x)

To solve the equation, remove the parenthesis by applying distributive property.

6( 72 × x - 72 × 2 ) = 4 × 15 - 4 × 3x

6( 72x - 144 ) = 60 - 12x

6( 72x - 144 ) = 60 - 12x

6 × 72x - 6 × 144 = 60 - 12x

432x - 864 = 60 - 12x

Collect like terms

Add -12x to both sides

432x + 12x - 864 = 60 - 12x + 12x

432x + 12x - 864 = 60

Add 864 to both sides

432x + 12x - 864 + 864 = 60 + 864

432x + 12x = 60 + 864

444x = 924

x = 924/444

x  = 77/37

Therefore, the value of x is 77/37.

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Answer:

5 Minutes and 56 Seconds

Step-by-step explanation:

Manjit= 1 Minute and 32.4 Seconds

Pierre = 1 Minute and 26.7 Seconds

Safia = 1 Minute and 25.1 Seconds

Chen = 1 Minute and 31.8 Seconds

4 X 1 Minute = 4 Minutes

32.4 + 26.7 +25.1 +31.8 = 116 or 1 Minute and 56 Seconds

Therefore, the answer is 5 Minutes and 56 Seconds

Answer:

Step-by-step explanation:

Sup dudes. I hear you need help... I don't know

The solution is given below in the attached diagram.

A histogram is an approximate representation of the distribution of numerical data. which is created in table form. The term was first introduced by Karl Pearson.

here, we have,

given that, The test scores of mrs Jackson 105 students are summarized in the table, now, we have to construct , and, label a frequency histogram of the data with an appropriate scale

To draw histogram, we first prepare the frequency distribution with boundary points, with central value of each class;

the required histogram is attached below.

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In order to determine whether a critical point of a loss function is a global minimum, it is necessary to consider the second derivative of the function.

If the second derivative is positive at the critical point, then we can say with certainty that the critical point is a local minimum. However, this does not necessarily mean that it is a function function. This is because there may be other local minima at points which the second derivative is negative, and in this case, the critical point must be compared to these points to determine if it is indeed the global minimum.

In order to assess whether a local minimum is a global minimum, we must first identify any other local minima. This can be done by locating the points at which the first derivative of the function is equal to zero and then evaluating the second derivative of the function at these points. If the second derivative is negative at any of the points, then we have identified a local minimum. Then, we can compare the value of the loss function at the points function as local minima to the value of the loss function at the critical point. If the value of the loss function at the critical point is lower than the value of the loss function at the other local minima, then the critical point is the global minimum. If the values are equal, then the critical point is a global minimum if and only if it is the only local minimum.Overall, identifying whether a critical point of a loss function is a global minimum requires both sufficiency and necessity. It is necessary to evaluate the second derivative of the function at the critical point in order to determine whether it is a local minimum, and it is also necessary to identify any other local minima and compare the value of the loss function at the critical point to the value of the function at the other local minima in order to determine whether the critical point is the global minimum.

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The 5th term of the arithmetic sequence is a₅ = 9/20

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the first term of the AP a₁ = 1/4

The second term of the AP is a₂ = 3/10

So , the common difference is d = 3/10 - 1/4 = 1/5

Now , the arithmetic progression will be

The 5th term of the AP a₅ = a + ( n - 1 ) d

Substitute the values in the equation , we get

The 5th term of the AP a₅ = 1/4 + ( 5 - 1 ) ( 1/5 )

On simplifying the equation , we get

The 5th term of the AP a₅ = 1/4 + 4/5

The 5th term of the AP a₅ = 9/20

Hence , the 5th term of the AP 9/20

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The value of $×$ is 3.14 units

Perimeter is the distance around the edge of a shape. The algebraic sum of the length of each side is the perimeter of that shape. We have formulas available for the various shapes in geometry.

The perimeter of a square is expressed as 4l

The circumference of a circle = 2πr

This means that;

4l = 2πr

4l = 2× 3.142 × 2

4l = 12.57

divide both sides by 4

l = 12.57/4

l = 3.14 units(nearest hundredth)

therefore the value of the side length is 3.14 units

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The positions of points is shown below.

A point in mathematics is symbolised by a dot (.) and used to indicate an accurate location in space. It lacks all three dimensions—length, width, and height. It has no size, in other terms. A point's name is typically written in all caps.

Given:

We have to mark a point in three position in according to the line.

First, point on line means point should be marked on the line.

Then, the point above the line means that the point should be located on the upper side of the line.

Lastly, the point below the line means that the point should be located on the lower side of the line.

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The estimate for the number of the paintings that are over 70 years old is given as follows:

68 paintings.

The histogram shows the number of observations that appear in each range of the data-set.

24 of the paintings in the gallery are over 90 years old, hence the height of each small square is of:

24/(3 x 4) = 2 units.

Then the estimate of those over 70 years old is given as follows:

Then the total amount is of:

2 x 22 + 24 = 68.

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The scale factor is found dividing one side length of the right triangle on the right by the equivalent side length on the right triangle on the left.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For this problem, we have that the original and the dilated figures are given as follows:

Hence the scale factor is found dividing one side length of the right triangle on the right by the equivalent side length on the right triangle on the left.

The problem is incomplete, hence the general procedure to obtain the scale factor was presented.

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A graph giving us a idea about relationship between the number of days and total amount of sunglasses is mentioned in the image attached below.

In this case, using Microsoft Excel, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot and the total number of sunglasses would be plotted on the y-axis (y-coordinate).

From the scatter plot (attached image) which shows the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 62

Hence, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days and total amount of sunglasses.

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Answer:C

Step-by-step explanation:

When bisecting a segment using a compass, Sasha's next step would be to swing an arc that intersects the segment. Correct option is B.

To bisect a segment, Sasha needs to find the midpoint of the segment. The compass can help her achieve this by creating two arcs with the same radius from each endpoint of the segment. The intersection of these arcs will be the midpoint of the segment.

Sasha's first step is to place the compass on one endpoint of the segment and open it to a width larger than the length of the segment. Then, she places the compass on the other endpoint and draws an arc that intersects the first arc.

The next step is to swing an arc with the same radius from the other endpoint of the segment, again intersecting the first arc. The intersection of these two arcs will give the midpoint of the segment, which can be marked with a straightedge.

Therefore, Sasha's next step in bisecting a segment using a compass is to swing an arc that intersects the segment.

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The required interior angle of 20-gon measures 162 degrees.

The interior angle measure for the n-sided polygon is given by
Interior angle measure = (n-2) x 180° / n, where n is the number of sides (or vertices) of the polygon.

Here,

To find the measure of each interior angle of a 20-gon (icosagon), we can use the formula:

For a 20-gon, n = 20. Substituting this into the formula, we get:

Interior angle measure = (20-2) x 180° / 20

= 18 x 180° / 20

= 162°

Therefore, each interior angle of 20-gon measures 162 degrees.

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Answer:

(2.571, 10.143)

Step-by-step explanation:

Answer:

(4, 3) ordered pair

Step-by-step explanation:

Rearranging the two equations making y the subject of the equations:

[tex]y = -5x + 23[/tex] —-(equation i)

[tex]y = 2x - 5[/tex] ——-(equation ii)

Equating equation i to equation ii and solve for x. Bring all the like terms together:

[tex]2x - 5 = -5x + 23[/tex]

[tex]= 2x + 5x = 23 + 5[/tex]

[tex]= 7x = 28[/tex]

x = [tex]\frac{28}{7}[/tex]

∴ x = 4

Substitute the value of x in any of the two equation to solve for y:[tex]y = 2(4) - 5[/tex]

y = [tex]8 - 5[/tex]

y = 3

Together these x and y values form an ordered pair, which is also the point of intersection for these two equations: [tex](4, 3)[/tex]

The height of the cell phone tower in feet will be 135 feet high.

The utilization of two or more additional numbers that compares is known as the ratio.

The cell tower that casts a shadow is 100 feet long.

Lia casts shadows 3 feet and 4 inches long.

If Lia is 4 feet 6 inches tall.

Let 'h' be the height of the tower. Then the height of the tower is given as,

h / 100 = (4 + 6/12) / (3 + 4/12)

h / 100 = 4.5 / 3.33

h / 100 = 1.35

h = 135 feet

The height of the cell phone tower in feet will be 135 feet high.

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If the amount of medication in the body decrease by a factor of 1/3 each hour , then the exponential function is y = 1.8(2/3)ˣ .

Let M = the initial amount of medication administered = 1.8 milliliters , and

Let y = the amount of medication remaining in the patient's body after x hours.

We know that the medication amount will decrease by a factor of 1/3 each hour, which means that after 1 hour, only (1-1/3) = 2/3  of the medication will remain, after 2 hours, only (2/3)² will remain, and so on.

So we can write the equation in exponential form as :

⇒ y = M × (1-1/3)ˣ

⇒ y = M × (2/3)ˣ ;

substituting the initial value as 1.8  ,

we get ;

⇒ y = 1.8 × (2/3)ˣ ;

where x = number of hours that have passed since the medication was administered.

Therefore , the exponential function for the situation is y = 1.8 × (2/3)ˣ  .

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The given question is incomplete , the complete question is

Elizabeth is a nurse, and she just administered 1.8 milliliters of medication to one of her patients. Elizabeth knows that the amount of medication remaining in the patient's body will decrease by a factor of 1/3 each hour .

Write an exponential equation in the form y = a(b)ˣ that can model the amount of medication (y) , remaining in the patient's body after x hours .

Answer:

Step-by-step explanation: